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A scatterplot with six plotted points.

Determine the reliability of the linear model given the residual plot.

(1 point)
Responses

The residual plot is equally and randomly distributed around the line where residual=0. Therefore, the linear regression model is a good choice for these data and will provide accurate results when making predictions.
The residual plot is equally and randomly distributed around the line where residual=0. Therefore, the linear regression model is a good choice for these data and will provide accurate results when making predictions.

The given residual plot clearly has a pattern. Therefore, the linear model is reliable and will provide accurate predictions for the original data.
The given residual plot clearly has a pattern. Therefore, the linear model is reliable and will provide accurate predictions for the original data.

The residual plot is equally and randomly distributed around the line where residual=0. Therefore, the linear regression model is not a good choice for these data and will not provide accurate results when making predictions.
The residual plot is equally and randomly distributed around the line where residual=0. Therefore, the linear regression model is not a good choice for these data and will not provide accurate results when making predictions.

The given residual plot clearly has a pattern. Therefore, the linear model is not reliable and will not provide accurate predictions for the original data.

1 answer

To determine the reliability of the linear model based on the information about the residual plot, we can consider the main principles of analyzing residuals.

  1. Residuals are the differences between observed and predicted values:
    • If the residuals are randomly distributed around zero, it indicates that the linear model is appropriate for the data.
    • If there is a distinct pattern in the residuals, it suggests that the linear model is not a good fit, and a different model may be more appropriate.

Based on this understanding, the appropriate response is:

"The given residual plot clearly has a pattern. Therefore, the linear model is not reliable and will not provide accurate predictions for the original data."

This response indicates that the presence of a pattern in the residuals suggests the linear model does not adequately capture the relationships in the data.